The length of AD is 32 feet
Step-by-step explanation:
An architect is sketching a blueprint of a patio for a new fence
- On the blueprint, C is the midpoint of segment AD
- Point B is the midpoint of segment AC
- BC = 8 feet
We need to find the length of AD
A mid-point divides a line segments into two equal parts in length
∵ C is the mid-point of AD
- The mid-point C divides the line segments AD into two equal parts
∴ AC = CD
∵ B is the mid point of AC
∴ AB = BC
∵ BC = 8 feet
∴ AB = 8 feet
- AC contains AB and BC
∵ AC = AB + BC
∴ AC = 8 + 8 = 16
∵ AC = CD
∵ AC = 16
∴ CD = 16
- AD contains AC and CD
∵ AD = AC + CD
∴ AD = 16 + 16 = 32
The length of AD is 32 feet
Learn more:
You can learn more about the mid-point in brainly.com/question/3269852
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Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
<h3><u>Part (a)</u></h3>
The cake can be modeled as a <u>cylinder </u>with:
- diameter = 9 in
- height = 4 in



<h3><u>Part (b)</u></h3>

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

<h3><u>Part (c)</u></h3>
The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

<h3><u>Part (d)</u></h3>
Probability is approximately 10.6% (see above for calculation)
<h3><u>Part (e)</u></h3>
If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
Answer:
f(-2) = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 3x + 1
f(-2) is x = -2
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: f(-2) = 3(-2) + 1
- Multiply: f(-2) = -6 + 1
- Add: f(-2) = -5
90/2 = 45 degrees twices
These both are 45 degrees which is less than 90
There is no picture with this so I don’t know how to answer this